The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?

Subtract the known addend from the sum, combining like terms: (8 − 2)d⁵ = 6d⁵, (−3 − (−1))c³d² = −2c³d², and (−4 − 8)cd⁴ = −12cd⁴. The c²d³ term remains 5c²d³, and 9 − 1 = 8, giving 6d⁵ − 2c³d² + 5c²d³ − 12cd⁴ + 8, choice A.

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